Week1 Bayesian Network
Graphcial representation¶
- Intuitive & Compact data structure
- Efficient reasoning using general-purpose algorithms
- Sparse Parameterization
- feasible elicitation
- learning from data
Applicationd¶
- Quiz
Marginal Distribution¶
Factor¶
Factor is a function of variables
Scope is a set of variables
Joint Distribution is a factor
$P(I,D,G) = \phi(I,D,G)$
- Conditional distribution is also a factor
- Facotr is not always about probabilities
Factor Reduction¶
- $\phi_1(C=1|A,B)$
- Like the conditional probability
Bayesian Network¶
- A Bayesian network is:
- A directed acyclic graph(DAG)G whose nodes represent the random variables $X_1,...,X_n$
- For each node $X_i$, we have a Conditional Probability Distribution(CPD) $P(X_i|Par_G(X_i))$
- The BN represents a joint distribution via the chain rule for bayesian networks $P(X1,...,X_n) = \prod_i P(X_i|Par_G(X_i))$
- Quiz
Prove BN¶
- we wanto prove Bayesian network is a valid probability (joint) distribution
- $> 0$ ,
- $\sum=1$
Flow of Probabilistic Influence¶
- Without evidence
- With evidence
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